Do I just hold back? Need advise about a friend?

It sounds like her mind is "pre occupied" with other things of some kind. If you know for a fact she is having problems at home, this just may be a big part of her problem. IF she doesn't want to talk about it or "share" things with you, there's nothing you can even do to be of help to her either. You've offered to be of help to her, but she's declined it. She knows how you feel about her as you've stated you've told her. It's now up to her as how much she's going to allow you into her life. Give her some space & if she needs you, she surely knows you're there for her.*